Multi-cornered strengthening members

ABSTRACT

A strengthening member for an automotive vehicle comprises an eight-cornered cross section including sides and corners. The sides comprise four straight sides and four curved sides. A length of each straight side ranges from about 10 mm to about 200 mm and a length of each curved side is about 10 mm to about 200 mm.

RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.13/087,633 (filed on Apr. 15, 2011; now U.S. Pat. No. 8,459,726), theentire contents of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present teachings relate generally to a strengthening member for avehicle body or other structures. The present teachings relate morespecifically to strengthening members having multi-cornered crosssections.

BACKGROUND OF THE INVENTION

It is desirable, for vehicle strengthening members, to maximize impactenergy absorption and bending resistance while minimizing mass per unitlength of the strengthening member.

When a compressive force is exerted on a strengthening member, forexample, a force due to a front impact load on a vehicle's front rail orother strengthening member in the engine compartment, the strengtheningmember can crush in a longitudinal direction to absorb the energy of thecollision. In addition, when a bending force is exerted on astrengthening member, for example a force due to a side impact load on avehicle's front side sill, B-pillar, or other strengthening member, thestrengthening member can bend to absorb the energy of the collision.

Strengthening members have traditionally had rectangular cross sections,with an axis of maximum moment of inertia aligned with a horizontal Yaxis (i.e., a lateral axis) of the member. During axial crush, however,rectangular strengthening members may be susceptible to inboard and/oroutboard bending (i.e., bending in the Y plane respectively towardand/or away from a vehicle centerline) about the axis of minimum momentof inertia (i.e., the vertical axis), thereby essentially providingunilateral resistance to bending. Consequently, to absorb crush energymore efficiently, a number of non-traditional strengthening member crosssections have been developed.

U.S. Pat. No. 6,588,830, for example, discloses a strengthening memberhaving a polygonal cross section of more than four sides, resulting ingreater reliability and higher energy absorbing efficiency. Astrengthening member with a basic octagonal cross section is disclosedas a preferred embodiment.

U.S. Pat. No. 6,752,451 discloses a strengthening member having concaveportions at the four corners of the basic rectangular cross section,resulting in four U-shaped portions forming an angle of 90 degrees witheach other. To avoid cracks at the concave portions at the four cornersand to increase strength, the concave portions have increased thicknessand hardness. Increased thickness and hardness of the corner portions isdisclosed to be achievable only by drawing or hydroforming, andtherefore decreases manufacturing feasibility while increasing the massper unit length of the strengthening member.

U.S. Pat. No. 6,752,451 makes reference to Japanese Unexamined PatentPublication No. H8-337183, which also discloses a strengthening memberhaving concave portions at the four corners of a basic rectangular crosssection, resulting in four U-shaped portions forming an angle of 90degrees with each other. U.S. Pat. No. 6,752,451 states that itsthickened concave portions provide improved crush resistance andflexural strength over H8-337183.

It may be desirable, therefore, to provide a variety of tunablestrengthening member cross sections configured to achieve strengthincreases (i.e., load carrying and energy absorption) over basicpolygonal designs, while also allowing flexibility in design to meet arange of vehicle applications. It also may be desirable to providestrengthening member configurations which achieve similar if not greaterstrength increases than members with thickened corners, while minimizingthe mass per unit length of a member and maintaining manufacturingfeasibility.

It may further be desirable to provide strengthening members that canachieve increased energy absorption and a more stable axial collapsewhen forces such as front and side impact forces are exerted on themember, while also conserving mass to reduce vehicle weights and meetemission requirements.

SUMMARY OF THE INVENTION

In accordance with certain embodiments, the present teachings provide astrengthening member for an automotive vehicle. The strengthening membercomprises an eight-cornered cross section including sides and corners.The sides comprise four straight sides and four curved sides. A lengthof each straight side ranges from about 10 mm to about 200 mm and alength of each curved side ranges from about 10 mm to about 200 mm.

In accordance with certain additional embodiments, the present teachingsprovide a strengthening member for an automotive vehicle. Thestrengthening member comprises a twelve-cornered cross section includingsides and corners. The sides comprise eight straight sides and fourcurved sides. A length of each straight side ranges from about 10 mm toabout 200 mm and a length of each curved side ranges from about 10 mm toabout 200 mm.

In accordance with certain additional embodiments, the present teachingsprovide a strengthening member for an automotive vehicle. Thestrengthening member comprises a fourteen-cornered cross sectionincluding sides and corners creating twelve internal angles and twoexternal angles. Each internal angle ranges from about 95 degrees toabout 145 degrees, and each external angle ranges from about 5 degreesto about 130 degrees.

In accordance with certain additional embodiments, the present teachingsprovide a strengthening member for an automotive vehicle. Thestrengthening member comprises a sixteen-cornered cross sectionincluding sides and corners creating twelve internal angles and fourexternal angles. Each internal angle ranges from about 25 degrees toabout 145 degrees and each external angle ranges from about 25 degreesto about 150 degrees.

In accordance with certain further embodiments, the present teachingsprovide a strengthening member for an automotive vehicle. Thestrengthening member comprises a twenty-cornered cross section includingsides and corners creating twelve internal angles and eight externalangles. Each internal angle ranges from about 25 degrees to about 145degrees and each external angle ranges from about 25 degrees to about150 degrees.

Additional objects and advantages will be set forth in part in thedescription which follows, and in part will be obvious from thedescription, or may be learned by practice of the present teachings. Theobjects and advantages of the teachings will be realized and attained bymeans of the elements and combinations particularly pointed out in theappended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate exemplary embodiments of theinvention and together with the description, serve to explain certainprinciples of the teachings.

BRIEF DESCRIPTION OF THE DRAWINGS

At least some features and advantages of the present teachings will beapparent from the following detailed description of exemplaryembodiments consistent therewith, which description should be consideredwith reference to the accompanying drawings, wherein:

FIG. 1 illustrates an exemplary embodiment of an eight-cornered crosssection, with four straight sides and four circular sides, for astrengthening member in accordance with the present teachings;

FIGS. 2A-2E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.1;

FIG. 3 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 4 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 3;

FIG. 5 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 3;

FIG. 6 is a graph of the crush force and associated axial crush distancefor exemplary strengthening members having the cross sections shown inFIG. 3;

FIG. 7 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 3;

FIG. 8 illustrates an exemplary embodiment of an eight-cornered crosssection, with four straight sides and four elliptical sides, for astrengthening member in accordance with the present teachings;

FIGS. 9A-9E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.8;

FIG. 10 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 11 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 10;

FIG. 12 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 10;

FIG. 13 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 10;

FIG. 14 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 10;

FIG. 15 illustrates an exemplary embodiment of a twelve-cornered crosssection, with eight straight sides and four circular sides, for astrengthening member in accordance with the present teachings;

FIGS. 16A-16E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.15;

FIG. 17 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 18 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 17;

FIG. 19 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 17;

FIG. 20 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 17;

FIG. 21 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 17;

FIG. 22 illustrates an exemplary embodiment of a twelve-cornered crosssection, with eight straight sides and four elliptical sides, for astrengthening member in accordance with the present teachings;

FIGS. 23A-23E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.22;

FIG. 24 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 25 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 24;

FIG. 26 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 24;

FIG. 27 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 24;

FIG. 28 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 24;

FIG. 29 illustrates an exemplary embodiment of a fourteen-cornered crosssection for a strengthening member in accordance with the presentteachings;

FIGS. 30A-30E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.29;

FIG. 31 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 32 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 31;

FIG. 33 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 31;

FIG. 34 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 31;

FIG. 35 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 31;

FIG. 36 illustrates fourteen-cornered strengthening members of varyingcross sections having substantially the same thickness, length andperimeter;

FIG. 37 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 36;

FIG. 38 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 36;

FIG. 39 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 36;

FIG. 40 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 36;

FIG. 41 illustrates an exemplary embodiment of a sixteen-cornered crosssection for a strengthening member in accordance with the presentteachings;

FIGS. 42A-42E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.41;

FIG. 43 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 44 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 43;

FIG. 45 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 43;

FIG. 46 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 43;

FIG. 47 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 43;

FIG. 48 illustrates sixteen-cornered strengthening members of varyingcross sections having substantially the same thickness, length andperimeter;

FIG. 49 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 48;

FIG. 50 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 48;

FIG. 51 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 48;

FIG. 52 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 48;

FIG. 53 illustrates an exemplary embodiment of another sixteen-corneredcross section for a strengthening member in accordance with the presentteachings;

FIGS. 54A-54E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.53;

FIG. 55 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 56 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 55;

FIG. 57 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 55;

FIG. 58 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 55;

FIG. 59 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 55;

FIG. 60 illustrates sixteen-cornered strengthening members of varyingcross sections having substantially the same thickness, length andperimeter;

FIG. 61 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 60;

FIG. 62 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 60;

FIG. 63 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 60;

FIG. 64 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 60;

FIG. 65 illustrates an exemplary embodiment of a twenty-cornered crosssection for a strengthening member in accordance with the presentteachings;

FIGS. 66A-66E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.65;

FIG. 67 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 68 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 67;

FIG. 69 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 67;

FIG. 70 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 67;

FIG. 71 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 67;

FIG. 72 illustrates twenty-cornered strengthening members of varyingcross sections having substantially the same thickness, length andperimeter;

FIG. 73 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 72;

FIG. 74 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 72;

FIG. 75 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 72;

FIG. 76 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 72;

FIG. 77 illustrates an exemplary embodiment of another twenty-corneredcross section for a strengthening member in accordance with the presentteachings;

FIGS. 78A-78E illustrate how tunable parameters in accordance with thepresent teachings can be utilized to modulate the cross section of FIG.77;

FIG. 79 illustrates strengthening members of varying cross sectionshaving substantially the same thickness, length and perimeter;

FIG. 80 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 79;

FIG. 81 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 79;

FIG. 82 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 79;

FIG. 83 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 79;

FIG. 84 illustrates twenty-cornered strengthening members of varyingcross sections having substantially the same thickness, length andperimeter;

FIG. 85 illustrates an exemplary axial collapse of the strengtheningmembers shown in FIG. 84;

FIG. 86 illustrates an exemplary dynamic crush of the strengtheningmembers shown in FIG. 84;

FIG. 87 is a graph of the crush force and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 84; and

FIG. 88 is a graph of the axial crush energy and associated axial crushdistance for exemplary strengthening members having the cross sectionsshown in FIG. 84.

Although the following detailed description makes reference toillustrative embodiments, many alternatives, modifications, andvariations thereof will be apparent to those skilled in the art.Accordingly, it is intended that the claimed subject matter be viewedbroadly.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying drawings. The variousexemplary embodiments are not intended to limit the disclosure. To thecontrary, the disclosure is intended to cover alternatives,modifications, and equivalents.

The present teachings contemplate providing strengthening members withmulti-cornered cross sections having substantially increased stiffnessthroughout the sides and corners without increasing thickness within thecorners. The strengthening members provide, for example, a variety oftunable parameters configured to achieve strength increases (i.e., loadcarrying and energy absorption) over basic polygonal designs (e.g.,polygonal strengthening member cross sections having less or the samenumber of sides), while also allowing design flexibility to meet a rangeof vehicle applications. The strengthening members in accordance withthe present teachings can achieve increased energy absorption and a morestable axial collapse when forces such as front and side impact forcesare exerted on the strengthening member. Furthermore, the side lengthsand configurations, and/or degrees of the internal and external angles,of the present teachings can achieve a similar, if not greater, strengthincrease as thickened corners, while minimizing mass per unit length ofthe member and maintaining a high manufacturing feasibility because themember can be formed by stamping, press forming, hydro-forming, molding,die casting, and extrusion.

Conventional strengthening members having basic polygonal crosssections, such as, square, rectangular, hexagonal and octagonal, etc.,are generally used due to their manufacturing feasibility. Becausestrengthening members with multi-cornered cross sections in accordancewith the present teachings have substantially increased strength andstiffness without requiring thicker corner portions, they also have ahigher manufacturing feasibility than previously-contemplated membersthat have thickened corners. While still providing a desired strength, astrengthening member in accordance with the present teachings can beformed in one or multiple sections by, for example, stamping, pressing,hydro-forming, molding, and extrusion. Thus-formed sections can bejoined via welding, adhesive, fastening, or other known joiningtechnologies.

Strengthening members in accordance with the present teachings cancomprise, for example, steel, advanced high strength steel (AHSS), ultrahigh strength steel (UHSS), next generation high strength steel (NGHSS),aluminum, magnesium, fiberglass, nylon, plastic, a composite or anyother suitable materials. Those of ordinary skill in the art wouldunderstand, for example, that the material used for a strengtheningmember may be chosen as desired based on intended application,strength/weight considerations, cost, and other design factors.

In various exemplary embodiments of the present teachings, astrengthening member may comprise an eight-cornered cross section havingfour straight sides and four curved sides. An exemplary embodiment of aneight-cornered cross section for a strengthening member in accordancewith the present teachings is illustrated, for example, in FIG. 1. Asillustrated, the cross section comprises four straight sides havinglengths Ss₁-Ss₄ and thicknesses Ts₁-Ts₄, and four circular sides havinglengths Sc₁-Sc₄ and thicknesses Tc₁-Tc₄. The side lengths andthicknesses can be varied (i.e., tuned) to achieve improved strength andother performance features (e.g., stability of folding pattern) comparedto existing octagonal cross sections. This strength improvement furtherobviates the need for increased corner thickness, which is an unexpectedand unpredicted benefit of fine-tuning the design parameters (e.g., sidelengths and thicknesses) of a strengthening member having an eight-sided(i.e., eight-cornered) cross section.

As shown in FIGS. 2A-2E, for example, in accordance with variousembodiments of the present teachings, the lengths Ss₁-Ss₄ and Sc₁-Sc₄ ofthe sides can be varied, as would be understood by one skilled in theart, for example in accordance with available packaging space within avehicle. Furthermore, although not shown, in a similar manner, thethicknesses Ts₁-Ts₄ and Tc₁-Tc₄ of the sides can be varied. Those ofordinary skill in the art would understand, however, that FIGS. 2A-2Eare exemplary only, and are provided merely to illustrate how designparameters can be utilized to modulate the cross section of theexemplary embodiment of FIG. 1. Thus, the present teachings contemplatevarious eight-cornered cross section configurations having variousshapes and dimensions (i.e., corner bend radii, side lengths and/orthicknesses), which can be adjusted based on space requirements and/orto control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each straight side (Ss₁-Ss₄) can range from about 10 mm to about 200mm and a length of each circular side (Sc₁-Sc₄) can range from about 10mm to about 200 mm. In certain additional embodiments, a thickness ofthe sides and corners can range from about 0.7 mm to about 6.0 mm; andin certain embodiments, the thickness of the sides is substantially thesame as the thickness of the corners. Furthermore, in accordance withcertain additional exemplary embodiments, the thickness of thestrengthening member may vary, for example, within one side or from sideto side to optimize the overall axial crush and bending performance.

To demonstrate the improved strength and performance features of aneight-cornered cross section in accordance with the present teachings,having four straight sides and four circular sides, compared to variousexisting cross section designs, exemplary strengthening members weremodeled and experimental test runs were conducted, as shown anddescribed below with reference to FIGS. 3-7.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 3. Tests were thenrun for each member to simulate an impact with the same rigid mass (e.g.an impactor), impact speed, and initial kinetic energy. As shown in FIG.4, the eight-cornered cross section in accordance with the presentteachings having four straight sides and four circular sidesdemonstrated the most stable axial collapse and the highest crash energyabsorption. Furthermore, as shown in FIG. 5, the eight-cornered crosssection in accordance with the present teachings also demonstrated theshortest crush distance and smallest folding length.

FIG. 6 illustrates the crush force (in Kn) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.3. As shown in FIG. 6, the strengthening member having an eight-corneredcross section with four straight sides and four circular sides couldsustain a much higher crushing force for a given resulting crushingdistance as compared with the square, hexagonal, circular and octagonalcross sections. In fact, an eight-cornered cross section in accordancewith the present teachings achieved about a 40% to about 45% increase incrash energy absorption as compared with a basic octagonal crosssection.

FIG. 7 illustrates the axial crush energy (in Kn-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 3. As shown in FIG. 7, thestrengthening member having an eight-cornered cross section with fourstraight sides and four circular sides could absorb the total kineticenergy of the impact (i.e., 22983 Kn-mm) over a much shorter distance ascompared with the square, hexagonal, circular and octagonal crosssections. In fact, an eight-cornered cross section in accordance withthe present teachings absorbed the full axial crush energy in about 60%of the axial crush distance as the basic octagonal cross section.

An additional exemplary embodiment of an eight-cornered cross sectionfor a strengthening member in accordance with the present teachings isillustrated in FIG. 8. As illustrated, the cross section comprises fourstraight sides having lengths Ss₁-Ss₄ and thicknesses Ts₁-Ts₄, and fourelliptical sides having lengths Sc₁-Sc₄ and thicknesses Tc₁-Tc₄. Asabove, the side lengths and thicknesses can be varied (i.e., tuned) toachieve improved strength and other performance features (e.g.,stability of folding pattern) compared to existing octagonal crosssections, and may further obviate the need for increased cornerthickness.

As shown in FIGS. 9A-9E, for example, in accordance with variousembodiments of the present teachings, the lengths Ss₁-Ss₄ and Sc₁-Sc₄and thicknesses Ts₁-Ts₄ and Tc₁-Tc₄ (see FIG. 9D showing a taperedcross-section) of the sides can be varied, as would be understood by oneskilled in the art, for example in accordance with available packagingspace within a vehicle. Those of ordinary skill in the art wouldunderstand, however, that FIGS. 9A-9E are exemplary only, and areprovided merely to illustrate how design parameters can be utilized tomodulate the cross section of the exemplary embodiment of FIG. 8. Thus,as above, the present teachings contemplate various eight-cornered crosssection configurations having various shapes and dimensions (i.e.,corner bend radii, side lengths and/or thicknesses), which can beadjusted based on space requirements and/or to control member collapsemodes.

In certain embodiments of the present teachings, for example, a lengthof each straight side (Ss₁-Ss₄) can range from about 10 mm to about 200mm and a length of each circular side (Sc₁-Sc₄) can range from about 10mm to about 200 mm. In certain additional embodiments, a thickness ofthe sides and corners can range from about 0.7 mm to about 6.0 mm; andin certain embodiments, the thickness of the sides is substantially thesame as the thickness of the corners. Furthermore, in accordance withcertain additional exemplary embodiments, the thickness of thestrengthening member may vary, for example, within one side or from sideto side to optimize the overall axial crush and bending performance.

To demonstrate the improved strength and performance features of aneight-cornered cross section in accordance with the present teachings,having four straight sides and four elliptical sides, compared tovarious existing cross section designs, exemplary strengthening memberswere modeled and experimental test runs were conducted, as shown anddescribed below with reference to FIGS. 10-14.

As above, strengthening members of varying shapes having the samethickness, length and perimeter (e.g., each part having a mass of about1.22 Kg) were modeled as illustrated in FIG. 10. Tests were then run foreach member to simulate an impact with the same rigid mass (e.g. animpactor), impact speed, and initial kinetic energy. As shown in FIG.11, the eight-cornered cross section in accordance with the presentteachings having four straight sides and four elliptical sidesdemonstrated the most stable axial collapse and the highest crash energyabsorption. Furthermore, as shown in FIG. 12, the eight-cornered crosssection in accordance with the present teachings also demonstrated theshortest crush distance and smallest folding length.

FIG. 13 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.10. As shown in FIG. 13, the strengthening member having aneight-cornered cross section with four straight sides and fourelliptical sides could sustain a much higher crushing force for a givenresulting crushing distance as compared with the square, hexagonal,circular and octagonal cross sections. In fact, as above, aneight-cornered cross section in accordance with the present teachingsachieved about a 35% to about 40% increase in crash energy absorption ascompared with a basic octagonal cross section.

FIG. 14 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 10. As shown in FIG. 14, thestrengthening member having an eight-cornered cross section with fourstraight sides and four elliptical sides could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the square, hexagonal, circular and octagonal crosssections. In fact, an eight-cornered cross section in accordance withthe present teachings absorbed the full axial crush energy in about 65%of the axial crush distance as the basic octagonal cross section.

Eight cornered cross sections in accordance with the present teachings(having four straight sides and four curved sides) may, therefore, allowimproved impact energy management over, for example, basic octagonalstrengthening member cross sections, while minimizing mass per unitlength.

In various additional exemplary embodiments, a strengthening member inaccordance with the present teachings may comprise a twelve-corneredcross section having eight straight sides and four curved sides. Anexemplary embodiment of a twelve-cornered cross section for astrengthening member in accordance with the present teachings isillustrated in FIG. 15. As illustrated, the cross section compriseseight straight sides having lengths Ss₁-Ss₈ and thicknesses Ts₁-Ts₈,four circular sides having lengths Sc₁-Sc₄ and thicknesses Tc₁-Tc₄, andtwelve internal corners with angles

_(i1)-

_(i12). The side lengths and thicknesses and internal corner angles canbe varied (i.e., tuned) to achieve improved strength and otherperformance features (e.g., stability of folding pattern) compared toexisting twelve-sided cross sections. This strength improvement furtherobviates the need for increased corner thickness, which is an unexpectedand unpredicted benefit of fine-tuning the design parameters (e.g., sidelengths, thicknesses, and internal angles) of a strengthening memberhaving an twelve-sided (i.e., twelve-cornered) cross section.

As shown in FIGS. 16A-16E, for example, in accordance with variousembodiments of the present teachings, the lengths Ss₁-Ss₈ and Sc₁-Sc₄ ofthe sides (see FIGS. 16A-16C) and the angles

_(i1)-

_(i12) of the internal angles (see FIGS. 16D and 16E) can be varied, aswould be understood by one skilled in the art, for example in accordancewith available packaging space within a vehicle. Furthermore, althoughnot shown, in a similar manner, the thicknesses Ts₁-Ts₈ and Tc₁-Tc₄ ofthe sides can be varied. Those of ordinary skill in the art wouldunderstand, however, that FIGS. 16A-16E are exemplary only, and areprovided merely to illustrate how design parameters can be utilized tomodulate the cross section of the exemplary embodiment of FIG. 15. Thus,the present teachings contemplate various twelve-cornered cross sectionconfigurations having various shapes and dimensions (i.e., corner bendradii, side lengths, thicknesses and/or internal angles), which can beadjusted based on space requirements and/or to control member collapsemodes.

In certain embodiments of the present teachings, for example, a lengthof each straight side (Ss₁-Ss₈) can range from about 10 mm to about 200mm and a length of each circular side (Sc₁-Sc₄) can range from about 10mm to about 200 mm. In certain additional embodiments, a thickness ofthe sides and corners can range from about 0.7 mm to about 6.0 mm; andin certain embodiments, the thickness of the sides is substantially thesame as the thickness of the corners. Furthermore, in accordance withcertain additional exemplary embodiments, the thickness of thestrengthening member may vary, for example, within one side or from sideto side to optimize the overall axial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 60 degrees to about 145 degrees.

To demonstrate the improved strength and performance features of atwelve-cornered cross section in accordance with the present teachings,having eight straight sides and four circular sides, compared to variousexisting cross section designs, exemplary strengthening members weremodeled and experimental test runs were conducted, as shown anddescribed below with reference to FIGS. 17-21.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 17. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 18, the twelve-cornered cross section in accordance with thepresent teachings having eight straight sides and four circular sidesdemonstrated the most stable axial collapse and the highest crash energyabsorption. Furthermore, as shown in FIG. 19, the twelve-cornered crosssection in accordance with the present teachings also demonstrated theshortest crush distance and smallest folding length.

FIG. 20 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.17. As shown in FIG. 20, the strengthening member having aneight-cornered cross section with eight straight sides and four circularsides could sustain a much higher crushing force for a given resultingcrushing distance as compared with the square, hexagonal, circular andoctagonal cross sections. In fact, a twelve-cornered cross section inaccordance with the present teachings also achieved about a 25% to about35% increase in crash energy absorption as compared with an existingtwelve-sided cross section.

FIG. 21 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 17. As shown in FIG. 21, thestrengthening member having a twelve-cornered cross section with eightstraight sides and four circular sides could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the square, hexagonal, circular and octagonal crosssections. In fact, a twelve-cornered cross section in accordance withthe present teachings also absorbed the full axial crush energy in about75% of the axial crush distance as the existing twelve-sided crosssection.

An additional exemplary embodiment of a twelve-cornered cross sectionfor a strengthening member in accordance with the present teachings isillustrated in FIG. 22. As illustrated, the cross section compriseseight straight sides having lengths Ss₁-Ss₈ and thicknesses Ts₁-Ts₈,four elliptical sides having lengths Sc₁-Sc₄ and thicknesses Tc₁-Tc₄,and twelve internal corners with angles

_(i1)-

_(i12). As above, the side lengths and thicknesses and internal cornerangles can be varied (i.e., tuned) to achieve improved strength andother performance features (e.g., stability of folding pattern) comparedto existing twelve-sided cross sections, and may further obviate theneed for increased corner thickness.

As shown in FIGS. 23A-23E, for example, in accordance with variousembodiments of the present teachings, the lengths Ss₁-Ss₈ and Sc₁-Sc₄ ofthe sides (see FIGS. 23A-23C) and the angles

_(i1)-

_(i12) of the internal angles (see FIGS. 23D and 23E) can be varied, aswould be understood by one skilled in the art, for example in accordancewith available packaging space within a vehicle. Furthermore, althoughnot shown, in a similar manner, the thicknesses Ts₁-Ts₈ and Tc₁-Tc₄ ofthe sides can be varied. Those of ordinary skill in the art wouldunderstand, however, that FIGS. 23A-23E are exemplary only, and areprovided merely to illustrate how design parameters can be utilized tomodulate the cross section of the exemplary embodiment of FIG. 22. Thus,as above, the present teachings contemplate various twelve-corneredcross section configurations having various shapes and dimensions (i.e.,corner bend radii, side lengths, thicknesses and/or internal angles),which can be adjusted based on space requirements and/or to controlmember collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each straight side (Ss₁-Ss₈) can range from about 10 mm to about 200mm and a length of each elliptical side (Sc₁-Sc₄) can range from about10 mm to about 200 mm. In certain additional embodiments, a thickness ofthe sides and corners can range from about 0.7 mm to about 6.0 mm; andin certain embodiments, the thickness of the sides is substantially thesame as the thickness of the corners. Furthermore, in accordance withcertain additional exemplary embodiments, the thickness of thestrengthening member may vary, for example, within one side or from sideto side to optimize the overall axial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 60 degrees to about 145 degrees.

To demonstrate the improved strength and performance features of atwelve-cornered cross section in accordance with the present teachings,having eight straight sides and four elliptical sides, compared tovarious existing cross section designs, exemplary strengthening memberswere modeled and experimental test runs were conducted, as shown anddescribed below with reference to FIGS. 24-28.

As above, strengthening members of varying shapes (i.e., cross sections)having the same thickness, length and perimeter (e.g., each part havinga mass of about 1.22 Kg) were modeled as illustrated in FIG. 24. Testswere then run for each member to simulate an impact with the same rigidmass (e.g. an impactor), impact speed, and initial kinetic energy. Asshown in FIG. 25, the twelve-cornered cross section in accordance withthe present teachings having eight straight sides and four ellipticalsides demonstrated the most stable axial collapse and the highest crashenergy absorption. Furthermore, as shown in FIG. 26, the twelve-corneredcross section in accordance with the present teachings also demonstratedthe shortest crush distance and smallest folding length.

FIG. 27 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.24. As shown in FIG. 27, the strengthening member having aneight-cornered cross section with eight straight sides and fourelliptical sides could sustain a much higher crushing force for a givenresulting crushing distance as compared with the square, hexagonal,circular and octagonal cross sections. In fact, once again, thetwelve-cornered cross section in accordance with the present teachingsachieved about a 25% to about 30% increase in crash energy absorption ascompared with the existing twelve-sided cross section.

FIG. 28 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 24. As shown in FIG. 28, thestrengthening member having a twelve-cornered cross section with eightstraight sides and four elliptical sides could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the square, hexagonal, circular and octagonal crosssections. And, once again, the twelve-cornered cross section inaccordance with the present teachings absorbed the full axial crushenergy in about 75% of the axial crush distance as the existingtwelve-sided cross section.

Twelve-cornered cross sections in accordance with the present teachings(having eight straight sides and four curved sides) may, therefore,allow improved impact energy management over, for example, basicpolygonal strengthening member cross sections and an existingtwelve-sided cross-section, while minimizing mass per unit length.

In various additional exemplary embodiments, a strengthening member inaccordance with the present teachings may comprise a fourteen-corneredcross section. An exemplary embodiment of a fourteen-cornered crosssection for a strengthening member in accordance with the presentteachings is illustrated in FIG. 29. As illustrated, the cross sectioncomprises fourteen sides having lengths S₁-S₁₄ and thicknesses T₁-T₁₄,twelve internal corners with angles

_(i1)-

_(i12), and two external corners with angles

_(e1) and

_(e2). The side lengths and thicknesses and internal and external cornerangles can be varied (i.e., tuned) to achieve improved strength andother performance features (e.g., stability of folding pattern) comparedto existing strengthening member cross sections. This strengthimprovement further obviates the need for increased corner thickness,which is an unexpected and unpredicted benefit of fine-tuning the designparameters (e.g., side lengths, thicknesses, internal angles, andexternal angles) of a strengthening member having a fourteen-sided(i.e., fourteen-cornered) cross section.

As shown in FIGS. 30A-30E, for example, in accordance with variousembodiments of the present teachings, the lengths S₁-S₁₄ (see FIG. 30B)and thicknesses T₁-T₁₄ (see FIG. 30E showing tapered sides) of the sidesand the angles

_(e1) and

_(e2) of the external angles (see FIGS. 30C and 30D) can be varied, aswould be understood by one skilled in the art, for example in accordancewith available packaging space within a vehicle. Furthermore, althoughnot shown, in a similar manner, the angles

_(i1)-

_(i12) of the internal angles can be varied. Those of ordinary skill inthe art would understand, however, that FIGS. 30A-30E are exemplaryonly, and are provided merely to illustrate how design parameters can beutilized to modulate the cross section of the exemplary embodiment ofFIG. 29. Thus, the present teachings contemplate variousfourteen-cornered cross section configurations having various shapes anddimensions (i.e., corner bend radii, side lengths, thicknesses, internalangles and/or external angles), which can be adjusted based on spacerequirements and/or to control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each side (S₁-S₁₄) can range from about 10 mm to about 200 mm. Incertain additional embodiments, a thickness of the sides and corners canrange from about 0.7 mm to about 6.0 mm; and in certain embodiments, thethickness of the sides is substantially the same as the thickness of thecorners. Furthermore, in accordance with certain additional exemplaryembodiments, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 95 degrees to about 145 degrees, and eachexternal angle (

_(e1) and

_(e2)) ranges from about 5 degrees to about 130 degrees.

To demonstrate the improved strength and performance features of afourteen-cornered cross section in accordance with the present teachingscompared to various existing cross section designs, exemplarystrengthening members were modeled and experimental test runs wereconducted, as shown and described below with reference to FIGS. 31-35.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 31. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 32, the fourteen-cornered cross section in accordance with thepresent teachings demonstrated the most stable axial collapse and thehighest crash energy absorption. Furthermore, as shown in FIG. 33, thefourteen-cornered cross section in accordance with the present teachingsalso demonstrated the shortest crush distance and smallest foldinglength.

FIG. 34 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.31. As shown in FIG. 34, the strengthening member having afourteen-cornered cross section could sustain a much higher crushingforce for a given resulting crushing distance as compared with thesquare, hexagonal, circular and octagonal cross sections.

FIG. 35 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 31. As shown in FIG. 35, thestrengthening member having a fourteen-cornered cross section couldabsorb the total kinetic energy of the impact (i.e., 22983 KN-mm) over amuch shorter distance as compared with the square, hexagonal, circularand octagonal cross sections.

To further demonstrate the improved strength and performance features ofa fourteen-cornered cross section in accordance with the presentteachings compared to basic fourteen-sided cross section designs, asabove, exemplary strengthening members were modeled and experimentaltest runs were conducted, as shown and described below with reference toFIGS. 36-40.

Strengthening members of varying shapes (i.e., fourteen-sided crosssections) having the same thickness, length and perimeter (e.g., eachpart having a mass of about 1.22 Kg) were modeled as illustrated in FIG.36. As above, tests were then run for each member to simulate an impactwith the same rigid mass (e.g. an impactor), impact speed, and initialkinetic energy. As shown in FIG. 37, the fourteen-cornered cross sectionin accordance with the present teachings demonstrated the most stableaxial collapse and the highest crash energy absorption. Furthermore, asshown in FIG. 38, the fourteen-cornered cross section in accordance withthe present teachings also demonstrated the shortest crush distance andsmallest folding length.

FIG. 39 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.36. As shown in FIG. 34, the strengthening member having afourteen-cornered cross section in accordance with the present teachingscould sustain a much higher crushing force for a given resultingcrushing distance as compared with the other fourteen-sided crosssections (i.e., a basic fourteen-sided polygon (tetradecagon) and afourteen-sided corrugated polygon). In fact, the fourteen-cornered crosssection in accordance with the present teachings achieved about a 35% toabout 45% increase in crash energy absorption as compared with thetetradecagon.

FIG. 40 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 36. As shown in FIG. 40, thestrengthening member having a fourteen-cornered cross section inaccordance with the present teachings could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the other fourteen-sided cross sections. In fact, thefourteen-cornered cross section in accordance with the present teachingsabsorbed the full axial crush energy in about 65% of the axial crushdistance as the tetradecagon.

Fourteen-cornered cross sections in accordance with the presentteachings may, therefore, allow improved impact energy management over,for example, basic polygonal strengthening member cross sections,including basic fourteen-sided polygonal cross sections, whileminimizing mass per unit length.

In various additional exemplary embodiments, a strengthening member inaccordance with the present teachings may comprise a sixteen-corneredcross section. An exemplary embodiment of a sixteen-cornered crosssection for a strengthening member in accordance with the presentteachings is illustrated in FIG. 41. As illustrated, the cross sectioncomprises sixteen sides having lengths S₁-S₁₆ and thicknesses T₁-T₁₆,twelve internal corners with angles

_(i1)-

_(i12), and four external corners with angles

_(e1)-

_(e4). The side lengths and thicknesses and internal and external cornerangles can be varied (i.e., tuned) to achieve improved strength andother performance features (e.g., stability of folding pattern) comparedto existing strengthening member cross sections. This strengthimprovement further obviates the need for increased corner thickness,which is an unexpected and unpredicted benefit of fine-tuning the designparameters (e.g., side lengths, thicknesses, internal angles, andexternal angles) of a strengthening member having a sixteen-sided (i.e.,sixteen-cornered) cross section.

As shown in FIGS. 42A-42E, for example, in accordance with variousembodiments of the present teachings, the lengths S₁-S₁₆ (see FIGS. 42Dand 42E) and thicknesses T₁-T₁₆ (see FIG. 42B showing tapered sides) ofthe sides and the angles

_(i1)-

_(i12) of the internal angles and the angles

_(e1)-

_(e4) of the external angles (see FIG. 42C) can be varied, as would beunderstood by one skilled in the art, for example in accordance withavailable packaging space within a vehicle. Those of ordinary skill inthe art would understand, however, that FIGS. 42A-42E are exemplaryonly, and are provided merely to illustrate how design parameters can beutilized to modulate the cross section of the exemplary embodiment ofFIG. 41. Thus, the present teachings contemplate varioussixteen-cornered cross section configurations having various shapes anddimensions (i.e., corner bend radii, side lengths, thicknesses, internalangles and/or external angles), which can be adjusted based on spacerequirements and/or to control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each side (S₁-S₁₆) can range from about 10 mm to about 200 mm. Incertain additional embodiments, a thickness of the sides and corners canrange from about 0.7 mm to about 6.0 mm; and in certain embodiments, thethickness of the sides is substantially the same as the thickness of thecorners. Furthermore, in accordance with certain additional exemplaryembodiments, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 25 degrees to about 145 degrees, and eachexternal angle (

_(e1)-

_(e4)) ranges from about 25 degrees to about 150 degrees.

To demonstrate the improved strength and performance features of asixteen-cornered cross section in accordance with the present teachingscompared to various existing cross section designs, exemplarystrengthening members were modeled and experimental test runs wereconducted, as shown and described below with reference to FIGS. 43-47.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 43. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 44, the sixteen-cornered cross section in accordance with thepresent teachings demonstrated the most stable axial collapse and thehighest crash energy absorption. Furthermore, as shown in FIG. 45, thesixteen-cornered cross section in accordance with the present teachingsalso demonstrated the shortest crush distance and smallest foldinglength.

FIG. 46 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.43. As shown in FIG. 46, the strengthening member having asixteen-cornered cross section could sustain a much higher crushingforce for a given resulting crushing distance as compared with thesquare, hexagonal, circular and octagonal cross sections.

FIG. 47 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 43. As shown in FIG. 47, thestrengthening member having a sixteen-cornered cross section couldabsorb the total kinetic energy of the impact (i.e., 22983 Kn-mm) over amuch shorter distance as compared with the square, hexagonal, circularand octagonal cross sections.

To further demonstrate the improved strength and performance features ofa sixteen-cornered cross section in accordance with the presentteachings compared to basic sixteen-sided cross section designs, asabove, exemplary strengthening members were modeled and experimentaltest runs were conducted, as shown and described below with reference toFIGS. 48-52.

Strengthening members of varying shapes (i.e., sixteen-sided crosssections) having the same thickness, length and perimeter (e.g., eachpart having a mass of about 1.22 Kg) were modeled as illustrated in FIG.48. As above, tests were then run for each member to simulate an impactwith the same rigid mass (e.g. an impactor), impact speed, and initialkinetic energy. As shown in FIG. 49, the sixteen-cornered cross sectionin accordance with the present teachings demonstrated the most stableaxial collapse and the highest crash energy absorption. Furthermore, asshown in FIG. 50, the sixteen-cornered cross section in accordance withthe present teachings also demonstrated the shortest crush distance andsmallest folding length.

FIG. 51 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.48. As shown in FIG. 51, the strengthening member having asixteen-cornered cross section in accordance with the present teachingscould sustain a much higher crushing force for a given resultingcrushing distance as compared with the other sixteen-sided crosssections (i.e., a basic sixteen-sided polygon (hexadecagon) and asixteen-sided corrugated polygon). In fact, the sixteen-cornered crosssection in accordance with the present teachings achieved about a 50% toabout 55% increase in crash energy absorption as compared with thehexadecagon.

FIG. 52 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 48. As shown in FIG. 52, thestrengthening member having a sixteen-cornered cross section inaccordance with the present teachings could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the other sixteen-sided cross sections. In fact, thesixteen-cornered cross section in accordance with the present teachingsabsorbed the full axial crush energy in about 55% of the axial crushdistance as the hexadecagon.

An additional exemplary embodiment of a sixteen-cornered cross sectionfor a strengthening member in accordance with the present teachings isillustrated in FIG. 53. As illustrated, the cross section comprisessixteen sides having lengths S₁-S₁₆ and thicknesses T₁-T₁₆, twelveinternal corners with angles

_(i1)-

_(i12), and four external corners with angles

_(e1)-

_(e4). As above, the side lengths and thicknesses and internal andexternal corner angles can be varied (i.e., tuned) to achieve improvedstrength and other performance features (e.g., stability of foldingpattern) compared to existing strengthening member cross sections, andmay further obviate the need for increased corner thickness.

As shown in FIGS. 54A-54E, for example, in accordance with variousembodiments of the present teachings, the lengths S₁-S₁₆(see FIGS.54A-54D) and thicknesses T₁-T₁₆ (see FIG. 54E showing tapered sides) ofthe sides and the angles

_(i1)-

_(i12) of the internal angles and the angles

_(e1)-

_(e4) of the external angles (see FIGS. 54A-54D) can be varied, as wouldbe understood by one skilled in the art, for example in accordance withavailable packaging space within a vehicle. Those of ordinary skill inthe art would understand, however, that FIGS. 54A-54E are exemplaryonly, and are provided merely to illustrate how design parameters can beutilized to modulate the cross section of the exemplary embodiment ofFIG. 53. Thus, as above, the present teachings contemplate varioussixteen-cornered cross section configurations having various shapes anddimensions (i.e., corner bend radii, side lengths, thicknesses, internalangles and/or external angles), which can be adjusted based on spacerequirements and/or to control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each side (S₁-S₁₆) can range from about 10 mm to about 200 mm. Incertain additional embodiments, a thickness of the sides and corners canrange from about 0.7 mm to about 6.0 mm; and in certain embodiments, thethickness of the sides is substantially the same as the thickness of thecorners. Furthermore, in accordance with certain additional exemplaryembodiments, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 25 degrees to about 145 degrees, and eachexternal angle (

_(e1)-

_(e4)) ranges from about 25 degrees to about 150 degrees.

As above, to demonstrate the improved strength and performance featuresof a sixteen-cornered cross section in accordance with the presentteachings compared to various existing cross section designs, exemplarystrengthening members were modeled and experimental test runs wereconducted, as shown and described below with reference to FIGS. 55-59.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 55. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 56, the sixteen-cornered cross section in accordance with thepresent teachings demonstrated the most stable axial collapse and thehighest crash energy absorption. Furthermore, as shown in FIG. 57, thesixteen-cornered cross section in accordance with the present teachingsalso demonstrated the shortest crush distance and smallest foldinglength.

FIG. 58 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.55. As shown in FIG. 58, the strengthening member having asixteen-cornered cross section could sustain a much higher crushingforce for a given resulting crushing distance as compared with thesquare, hexagonal, circular and octagonal cross sections.

FIG. 59 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 55. As shown in FIG. 59, thestrengthening member having a sixteen-cornered cross section couldabsorb the total kinetic energy of the impact (i.e., 22983 Kn-mm) over amuch shorter distance as compared with the square, hexagonal, circularand octagonal cross sections.

As above, to further demonstrate the improved strength and performancefeatures of a sixteen-cornered cross section in accordance with thepresent teachings compared to basic sixteen-sided cross section designs,exemplary strengthening members were modeled and experimental test runswere conducted, as shown and described below with reference to FIGS.60-64.

Strengthening members of varying shapes (i.e., sixteen-sided crosssections) having the same thickness, length and perimeter (e.g., eachpart having a mass of about 1.22 Kg) were modeled as illustrated in FIG.60. As above, tests were then run for each member to simulate an impactwith the same rigid mass (e.g. an impactor), impact speed, and initialkinetic energy. As shown in FIG. 61, the sixteen-cornered cross sectionin accordance with the present teachings demonstrated the most stableaxial collapse and the highest crash energy absorption. Furthermore, asshown in FIG. 62, the sixteen-cornered cross section in accordance withthe present teachings also demonstrated the shortest crush distance andsmallest folding length.

FIG. 63 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.60. As shown in FIG. 63, once again, the strengthening member having asixteen-cornered cross section in accordance with the present teachingscould sustain a much higher crushing force for a given resultingcrushing distance as compared with the other sixteen-sided crosssections (i.e., the basic sixteen-sided polygon (hexadecagon) andsixteen-sided corrugated polygon). In fact, the sixteen-cornered crosssection in accordance with the present teachings achieved about a 50% toabout 60% increase in crash energy absorption as compared with thehexadecagon.

FIG. 64 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 60. As shown in FIG. 64, onceagain, the strengthening member having a sixteen-cornered cross sectionin accordance with the present teachings could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the other sixteen-sided cross sections. In fact, thesixteen-cornered cross section in accordance with the present teachingsabsorbed the full axial crush energy in about 50% of the axial crushdistance as the hexadecagon.

Sixteen-cornered cross sections in accordance with the present teachingsmay, therefore, allow improved impact energy management over, forexample, basic polygonal strengthening member cross sections, includingbasic sixteen-sided polygonal cross sections, while minimizing mass perunit length.

In various additional exemplary embodiments, a strengthening member inaccordance with the present teachings may comprise a twenty-corneredcross section. An exemplary embodiment of a twenty-cornered crosssection for a strengthening member in accordance with the presentteachings is illustrated in FIG. 65. As illustrated, the cross sectioncomprises twenty sides having lengths S₁-S₂₀ and thicknesses T₁-T₂₀,twelve internal corners with angles

_(i1)-

_(i12), and eight external corners with angles

_(e1)-

_(e8). The side lengths and thicknesses and internal and external cornerangles can be varied (i.e., tuned) to achieve improved strength andother performance features (e.g., stability of folding pattern) comparedto existing strengthening member cross sections. This strengthimprovement further obviates the need for increased corner thickness,which is an unexpected and unpredicted benefit of fine-tuning the designparameters (e.g., side lengths, thicknesses, internal angles, andexternal angles) of a strengthening member having a sixteen-sided (i.e.,twenty-cornered) cross section.

As shown in FIGS. 66A-66E, for example, in accordance with variousembodiments of the present teachings, the lengths S₁-S₂₀ (see FIG. 66A)and thicknesses T₁-T₂₀ (see FIGS. 66B and 66E showing tapered sides) ofthe sides and the angles

_(i1)-

_(i12) of the internal angles and the angles

_(e1)-

_(e8) of the external angles (see FIGS. 66B and 66D) can be varied, aswould be understood by one skilled in the art, for example in accordancewith available packaging space within a vehicle. Those of ordinary skillin the art would understand, however, that FIGS. 66A-66E are exemplaryonly, and are provided merely to illustrate how design parameters can beutilized to modulate the cross section of the exemplary embodiment ofFIG. 65. Thus, the present teachings contemplate various twenty-corneredcross section configurations having various shapes and dimensions (i.e.,corner bend radii, side lengths, thicknesses, internal angles and/orexternal angles), which can be adjusted based on space requirementsand/or to control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each side (S₁-S₂₀) can range from about 10 mm to about 200 mm. Incertain additional embodiments, a thickness of the sides and corners canrange from about 0.7 mm to about 6.0 mm; and in certain embodiments, thethickness of the sides is substantially the same as the thickness of thecorners. Furthermore, in accordance with certain additional exemplaryembodiments, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 25 degrees to about 145 degrees, and eachexternal angle (

_(e1)-

_(e8)) ranges from about 25 degrees to about 150 degrees.

To demonstrate the improved strength and performance features of atwenty-cornered cross section in accordance with the present teachingscompared to various existing cross section designs, exemplarystrengthening members were modeled and experimental test runs wereconducted, as shown and described below with reference to FIGS. 67-71.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 67. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 68, the twenty-cornered cross section in accordance with thepresent teachings demonstrated the most stable axial collapse and thehighest crash energy absorption. Furthermore, as shown in FIG. 69, thetwenty-cornered cross section in accordance with the present teachingsalso demonstrated the shortest crush distance and smallest foldinglength.

FIG. 70 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.67. As shown in FIG. 70, the strengthening member having atwenty-cornered cross section could sustain a much higher crushing forcefor a given resulting crushing distance as compared with the square,hexagonal, circular, octagonal, and existing twelve-cornered crosssections.

FIG. 71 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 67. As shown in FIG. 71, thestrengthening member having a twenty-cornered cross section could absorbthe total kinetic energy of the impact (i.e., 22983 Kn-mm) over a muchshorter distance as compared with the square, hexagonal, circular,octagonal, and existing twelve-cornered cross sections.

To further demonstrate the improved strength and performance features ofa twenty-cornered cross section in accordance with the present teachingscompared to basic twenty-sided cross section designs, as above,exemplary strengthening members were modeled and experimental test runswere conducted, as shown and described below with reference to FIGS.72-76.

Strengthening members of varying shapes (i.e., twenty-sided crosssections) having the same thickness, length and perimeter (e.g., eachpart having a mass of about 1.22 Kg) were modeled as illustrated in FIG.72. As above, tests were then run for each member to simulate an impactwith the same rigid mass (e.g. an impactor), impact speed, and initialkinetic energy. As shown in FIG. 73, the twenty-cornered cross sectionin accordance with the present teachings demonstrated the most stableaxial collapse and the highest crash energy absorption. Furthermore, asshown in FIG. 74, the twenty-cornered cross section in accordance withthe present teachings also demonstrated the shortest crush distance andsmallest folding length.

FIG. 75 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.72. As shown in FIG. 75, the strengthening member having atwenty-cornered cross section in accordance with the present teachingscould sustain a much higher crushing force for a given resultingcrushing distance as compared with the other twenty-sided cross sections(i.e., a basic twenty-sided polygon (icosagon) and a twenty-sidedcorrugated polygon). In fact, the twenty-cornered cross section inaccordance with the present teachings achieved about a 55% to about 65%increase in crash energy absorption as compared with the icosagon.

FIG. 76 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 72. As shown in FIG. 76, thestrengthening member having a twenty-cornered cross section inaccordance with the present teachings could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the other twenty-sided cross sections. In fact, thetwenty-cornered cross section in accordance with the present teachingsabsorbed the full axial crush energy in about 45% of the axial crushdistance as the icosagon.

An additional exemplary embodiment of a twenty-cornered cross sectionfor a strengthening member in accordance with the present teachings isillustrated in FIG. 77. As illustrated, the cross section comprisestwenty sides having lengths S₁-S₂₀ and thicknesses T₁-T₂₀, twelveinternal corners with angles

_(i1)-

_(i12), and eight external corners with angles

_(e1)-

_(e8). As above, the side lengths and thicknesses and internal andexternal corner angles can be varied (i.e., tuned) to achieve improvedstrength and other performance features (e.g., stability of foldingpattern) compared to existing strengthening member cross sections, andmay further obviate the need for increased corner thickness.

As shown in FIGS. 78A-78E, for example, in accordance with variousembodiments of the present teachings, the lengths S₁-S₂₀ (see FIGS.78A-78D) and thicknesses T₁-T₂₀ (see FIG. 78E showing tapered sides) ofthe sides and the angles

_(i1)-

_(i12) of the internal angles and the angles

_(e1)-

_(e8) of the external angles (see FIGS. 78A-78D) can be varied, as wouldbe understood by one skilled in the art, for example in accordance withavailable packaging space within a vehicle. Those of ordinary skill inthe art would understand, however, that FIGS. 78A-78E are exemplaryonly, and are provided merely to illustrate how design parameters can beutilized to modulate the cross section of the exemplary embodiment ofFIG. 77. Thus, as above, the present teachings contemplate varioustwenty-cornered cross section configurations having various shapes anddimensions (i.e., corner bend radii, side lengths, thicknesses, internalangles and/or external angles), which can be adjusted based on spacerequirements and/or to control member collapse modes.

In certain embodiments of the present teachings, for example, a lengthof each side (S₁-S₂₀) can range from about 10 mm to about 200 mm. Incertain additional embodiments, a thickness of the sides and corners canrange from about 0.7 mm to about 6.0 mm; and in certain embodiments, thethickness of the sides is substantially the same as the thickness of thecorners. Furthermore, in accordance with certain additional exemplaryembodiments, the thickness of the strengthening member may vary, forexample, within one side or from side to side to optimize the overallaxial crush and bending performance.

In certain embodiments of the present teachings, each internal angle (

_(i1)-

_(i12)) ranges from about 25 degrees to about 145 degrees, and eachexternal angle (

_(e1)-

_(e8)) ranges from about 25 degrees to about 150 degrees.

As above, to demonstrate the improved strength and performance featuresof a twenty-cornered cross section in accordance with the presentteachings compared to various existing cross section designs, exemplarystrengthening members were modeled and experimental test runs wereconducted, as shown and described below with reference to FIGS. 79-83.

Strengthening members of varying shapes (i.e., cross sections) havingthe same thickness, length and perimeter (e.g., each part having a massof about 1.22 Kg) were modeled as illustrated in FIG. 79. Tests werethen run for each member to simulate an impact with the same rigid mass(e.g. an impactor), impact speed, and initial kinetic energy. As shownin FIG. 80, the twenty-cornered cross section in accordance with thepresent teachings demonstrated the most stable axial collapse and thehighest crash energy absorption. Furthermore, as shown in FIG. 81, thetwenty-cornered cross section in accordance with the present teachingsalso demonstrated the shortest crush distance and smallest foldinglength.

FIG. 82 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.79. As shown in FIG. 82, the strengthening member having atwenty-cornered cross section could sustain a much higher crushing forcefor a given resulting crushing distance as compared with the square,hexagonal, circular, octagonal, and existing twelve-sided crosssections.

FIG. 83 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 79. As shown in FIG. 83, thestrengthening member having a twenty-cornered cross section could absorbthe total kinetic energy of the impact (i.e., 22983 KN-mm) over a muchshorter distance as compared with the square, hexagonal, circular,octagonal, and existing twelve-cornered cross sections.

As above, to further demonstrate the improved strength and performancefeatures of a twenty-cornered cross section in accordance with thepresent teachings compared to basic twenty-sided cross section designs,exemplary strengthening members were modeled and experimental test runswere conducted, as shown and described below with reference to FIGS.84-88.

Strengthening members of varying shapes (i.e., twenty-sided crosssections) having the same thickness, length and perimeter (e.g., eachpart having a mass of about 1.22 Kg) were modeled as illustrated in FIG.84. As above, tests were then run for each member to simulate an impactwith the same rigid mass (e.g. an impactor), impact speed, and initialkinetic energy. As shown in FIG. 85, the twenty-cornered cross sectionin accordance with the present teachings demonstrated the most stableaxial collapse and the highest crash energy absorption. Furthermore, asshown in FIG. 86, the twenty-cornered cross section in accordance withthe present teachings also demonstrated the shortest crush distance andsmallest folding length.

FIG. 87 illustrates the crush force (in KN) and associated axial crushdistance (in mm) for the simulated impact, exerted axially on theexemplary strengthening members having the cross sections shown in FIG.84. As shown in FIG. 87, once again, the strengthening member having atwenty-cornered cross section in accordance with the present teachingscould sustain a much higher crushing force for a given resultingcrushing distance as compared with the other twenty-sided cross sections(i.e., the basic twenty-sided polygon (icosagon) and twenty-sidedcorrugated polygon). In fact, the twenty-cornered cross section inaccordance with the present teachings achieved about a 60% to about 70%increase in crash energy absorption as compared with the icosagon.

FIG. 88 illustrates the axial crush energy (in KN-mm) and associatedaxial crush distance (in mm) for the exemplary strengthening membershaving the cross sections shown in FIG. 84. As shown in FIG. 88, onceagain, the strengthening member having a twenty-cornered cross sectionin accordance with the present teachings could absorb the total kineticenergy of the impact (i.e., 22983 KN-mm) over a much shorter distance ascompared with the other twenty-sided cross sections. In fact, thetwenty-cornered cross section in accordance with the present teachingsabsorbed the full axial crush energy in about 43% of the axial crushdistance as the icosagon.

Twenty-cornered cross sections in accordance with the present teachingsmay, therefore, allow improved impact energy management over, forexample, basic polygonal strengthening member cross sections, includingbasic twenty-sided polygonal cross sections, while minimizing mass perunit length.

Thus, as illustrated by the above exemplary embodiments, strengtheningmembers in accordance with the present teachings are configured toachieve strength increases (i.e., load carrying and energy absorption)over basic polygonal designs (including polygonal strengthening membercross sections having the same number of sides), while also permittingflexibility in design to better meet vehicle space requirements.Strengthening members in accordance with the present teachings may,therefore, be used to replace existing strengthening member crosssection designs (both traditional and non-traditional). While thepresent teachings have been disclosed in terms of exemplary embodimentsin order to facilitate a better understanding, it should be appreciatedthat the present teachings can be embodied in various ways withoutdeparting from the scope thereof. Therefore, the invention should beunderstood to include all possible embodiments which can be embodiedwithout departing from the scope of the invention set out in theappended claims.

Various exemplary embodiments of the present teachings contemplate, forexample, strengthening members with corners having different bend radii,with non-uniform cross sections (e.g., having non-symmetrical shapes),and/or with sides having variable thicknesses (i.e., having taperedsides). Various additional exemplary embodiments contemplatestrengthening members that are bent and/or curved. Moreover, to furtheradjust a member's folding pattern and/or peak load capacity, variousadditional exemplary embodiments also contemplate strengthening membershaving trigger holes, flanges, and/or convolutions as would beunderstood by those of ordinary skill in the art.

Furthermore, multi-cornered strengthening members in accordance with thepresent teachings are contemplated for use with a number of structuralmembers, such as, for example, crush cans, front rails, mid-rails, rearrails, side rails, shotguns, cross members, roof structures, beltlinetubes, door beams, pillars, internal reinforcements, and othercomponents that can benefit from increased crash energy absorption. Inaddition, the present teachings can be applied to both body-on-frame andunitized vehicles, or other types of structures. Thus, depending onapplication, embodiments of the present teachings will have variedshapes (i.e. various cross sections) to accommodate specific memberspace constraints. When used as a vehicle front rail, for example, toachieve optimized axial crush performance, the lengths and thicknessesof the sides and/or angles of the corners can all be adjusted (tuned) toprovide optimal strength, size and shape to meet engine compartmentconstraints.

Although various exemplary embodiments described herein have beendescribed as configured to be used with automotive vehicles, it isenvisioned that the various strengthening members in accordance with thepresent teachings may be configured for use with other types of vehiclesand/or structures, for which it may be desirable to provide increasedcrash energy absorption. Thus, it will be appreciated by those ofordinary skill in the art having the benefit of this disclosure that thepresent teachings provide strengthening members for variousapplications. Further modifications and alternative embodiments ofvarious aspects of the present teachings will be apparent to thoseskilled in the art in view of this description.

It is to be understood that the particular examples and embodiments setforth herein are non-limiting, and modifications to structure,dimensions, materials, and methodologies may be made without departingfrom the scope of the present teachings.

For the purposes of this specification and appended claims, unlessotherwise indicated, all numbers expressing quantities, percentages orproportions, and other numerical values used in the specification andclaims, are to be understood as being modified in all instances by theterm “about.” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in the written description and claims areapproximations that may vary depending upon the desired propertiessought to be obtained by the present invention. At the very least, andnot as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the present teachings are approximations, thenumerical values set forth in the specific examples are reported asprecisely as possible. Any numerical value, however, inherently containscertain errors necessarily resulting from the standard deviation foundin their respective testing measurements. Moreover, all ranges disclosedherein are to be understood to encompass any and all sub-ranges subsumedtherein.

It is noted that, as used in this specification and the appended claims,the singular forms “a,” “an,” and “the,” include plural referents unlessexpressly and unequivocally limited to one referent. As used herein, theterm “include” and its grammatical variants are intended to benon-limiting, such that recitation of items in a list is not to theexclusion of other like items that can be substituted or added to thelisted items.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the devices and methods ofthe present disclosure without departing from the scope of itsteachings. Other embodiments of the disclosure will be apparent to thoseskilled in the art from consideration of the specification and practiceof the teachings disclosed herein. It is intended that the specificationand embodiment described herein be considered as exemplary only.

What is claimed is:
 1. A method for manufacturing a strengthening memberfor an automotive vehicle, the strengthening member comprising aneight-cornered cross section including four straight sides and fourcurved sides, the method comprising: fabricating two or more sections ofthe strengthening member; and joining the two or more sections to formthe strengthening member comprising the eight-cornered cross sectionincluding four straight sides and four curved sides.
 2. The method ofclaim 1, wherein fabricating the two or more sections comprisesstamping, pressing, hyrdroforming, molding, and/or extruding each of thetwo or more sections.
 3. The method of claim 1, wherein fabricating thetwo or more sections comprises fabricating each section to form at leastone corner having substantially a same thickness as at least two sidesof the respective section.
 4. The method of claim 1, wherein joining thetwo or more sections comprises joining the two or more sections by oneor more of welding, adhesion, and fastening.
 5. The method of claim 1,wherein joining the two or more sections comprises forming thestrengthening member comprising the eight-cornered cross section, witheach of the straight sides having a length ranging from about 10 mm toabout 200 mm and each of the curved sides having a length ranging fromabout 10 mm to about 200 mm.
 6. A method for manufacturing astrengthening member for an automotive vehicle, the strengthening membercomprising a twelve-cornered cross section including eight straightsides and four curved sides, the method comprising: fabricating two ormore sections of the strengthening member; and joining the two or moresections to form the strengthening member comprising the twelve-corneredcross section including eight straight sides and four curved sides. 7.The method of claim 6, wherein fabricating the two or more sectionscomprises stamping, pressing, hyrdroforming, molding, and/or extrudingeach of the two or more sections.
 8. The method of claim 6, whereinjoining the two or more sections comprises joining the two or moresections by one or more of welding, adhesion, and fastening.
 9. Themethod of claim 6, wherein fabricating the two or more sectionscomprises fabricating each section to form at least one corner havingsubstantially a same thickness as at least two sides of the respectivesection.
 10. The method of claim 6, wherein joining the two or moresections comprises forming the strengthening member comprising thetwelve-cornered cross section, with each of the straight sides having alength ranging from about 10 mm to about 200 mm and each of the curvedsides having a length ranging from about 10 mm to about 200 mm.
 11. Amethod for manufacturing a strengthening member for an automotivevehicle, the strengthening member comprising a fourteen-cornered crosssection including sides and corners creating twelve internal angles andtwo external angles, the method comprising: fabricating two or moresections of the strengthening member; and joining the two or moresections to form the strengthening member comprising thefourteen-cornered cross section including sides and corners creatingtwelve internal angles and two external angles.
 12. The method of claim11, wherein fabricating the two or more sections comprises stamping,pressing, hyrdroforming, molding, and/or extruding each of the two ormore sections.
 13. The method of claim 11, wherein joining the two ormore sections comprises joining the two or more sections by one or moreof welding, adhesion, and fastening.
 14. The method of claim 11, whereinfabricating the two or more sections comprises fabricating each sectionto form at least one corner having substantially a same thickness as atleast two of the sides of the respective section.
 15. The method ofclaim 11, wherein joining the two or more sections comprises forming thestrengthening member comprising the fourteen-cornered cross section,with each of the internal angles ranging from about 95 degrees to about145 degrees and each of the external angles ranging from about 5 degreesto about 130 degrees.
 16. The method of claim 11, wherein joining thetwo or more sections comprises forming the strengthening member suchthat the strengthening member has a substantially uniform cross-sectionor has a continuous taper along a substantial length of thestrengthening member from a first end of the strengthening member to asecond end of the strengthening member.
 17. A method for manufacturing astrengthening member for an automotive vehicle, the strengthening membercomprising a sixteen-cornered cross section including sides and cornerscreating twelve internal angles and four external angles, the methodcomprising: fabricating two or more sections of the strengtheningmember; and joining the two or more sections to form the strengtheningmember comprising the sixteen-cornered cross section including sides andcorners creating twelve internal angles and four external angles. 18.The method of claim 17, wherein fabricating the two or more sectionscomprises stamping, pressing, hyrdroforming, molding, and/or extrudingeach of the two or more sections.
 19. The method of claim 17, whereinjoining the two or more sections comprises joining the two or moresections by one or more of welding, adhesion, and fastening.
 20. Themethod of claim 17, wherein fabricating the two or more sectionscomprises fabricating each section to form at least one corner havingsubstantially a same thickness as at least two of the sides of therespective section.
 21. The method of claim 17, wherein joining the twoor more sections comprises forming the strengthening member comprisingthe sixteen-cornered cross section, with each of the internal anglesranging from about 25 degrees to about 145 degrees and each of theexternal angles ranging from about 25 degrees to about 150 degrees. 22.The method of claim 17, wherein joining the two or more sectionscomprises forming the strengthening member such that the strengtheningmember has a substantially uniform cross-section or has a continuoustaper along a substantial length of the strengthening member from afirst end of the strengthening member to a second end of thestrengthening member.
 23. A method for manufacturing a strengtheningmember for an automotive vehicle, the strengthening member comprising atwenty-cornered cross section including sides and corners creatingtwelve internal angles and eight external angles, the method comprising:fabricating two or more sections of the strengthening member; andjoining the two or more sections to form the strengthening membercomprising the sixteen-cornered cross section including sides andcorners creating twelve internal angles and eight external angles. 24.The method of claim 23, wherein fabricating the two or more sectionscomprises stamping, pressing, hyrdroforming, molding, and/or extrudingeach of the two or more sections.
 25. The method of claim 23, whereinjoining the two or more sections comprises joining the two or moresections by one or more of welding, adhesion, and fastening.
 26. Themethod of claim 23, wherein fabricating the two or more sectionscomprises fabricating each section to form at least one corner havingsubstantially a same thickness as at least two of the sides of therespective section.
 27. The method of claim 23, wherein joining the twoor more sections comprises forming the strengthening member comprisingthe twenty-cornered cross section, with each of the internal anglesranging from about 25 degrees to about 145 degrees and each of theexternal angles ranging from about 25 degrees to about 150 degrees. 28.A method for increasing an axial compression strength of a strengtheningmember for an automotive vehicle without increasing a weight of thestrengthening member, the method comprising: tuning one or moreparameters of the strengthening member to substantially increase astiffness throughout sides and corners of the strengthening memberwithout increasing a thickness of the corners of the strengtheningmember; and modulating a cross section of the strengthening member basedon the one or more parameters.
 29. The method of claim 28, whereintuning the one or more parameters comprises tuning lengths of the sidesof the strengthening member, thicknesses of the sides and corners of thestrengthening member, and/or degrees of internal and external anglescreated by the sides and corners of the strengthening member.
 30. Themethod of claim 28, wherein tuning the lengths of the sides comprisesadjusting a length of each side within a range of about 5 mm to about200 mm.
 31. The method of claim 28, wherein tuning the thicknesses ofthe sides comprises adjusting a thickness of each side within a range ofabout 0.7 mm to about 6.0 mm.
 32. The method of claim 28, wherein tuningthe thicknesses of the corners comprises adjusting a thickness of eachcorner within a range of about 0.7 mm to about 6.0 mm.
 33. The method ofclaim 28, wherein tuning the thicknesses of the corners comprisesadjusting a thickness of each corner to have substantially the samethickness as each side.
 34. The method of claim 28, wherein tuning thedegrees of internal and external angles comprises adjusting eachinternal angle within a range of about 25 degrees to about 145 degreesand adjusting each external angle within a range of about 5 degrees toabout 150 degrees.
 35. The method of claim 28, wherein modulating across section comprises modulating a polygonal cross section.
 36. Themethod of claim 28, wherein modulating a cross section comprisesmodulating an eight-cornered cross section, a twelve-cornered crosssection, a fourteen-cornered cross section, a sixteen-cornered crosssection and/or a twenty-cornered cross-section.